An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 39
. 22 ELEMENTARY THEOREMS Ex. 10. li A, B, C, D he any four points, and x any straight line, provethat (BOB). Ax-{CDA). Bx+{DAB). Cx-{ABO . Dx=0. … Let AD cut BC in the point 0, then, by § 28, we haveBC.Ox+CO.Bx+OB.Cx=0,and AD.Ox + DO.Ax + OA.Dx=0. Hence DO. BC. Ax-CO. AD. Bx-OB.AD. Cx+OA . BC. Dx=0 ;or DO. BC. Ax+DA. CO.Bx-BO. DA . Cx-BC. AO. Dx=0. But {BCD)=iDO. 5C. sin BOD, {CDA)=iDA. CO.sin AOC, (DAB) = iDA. BO. siaAOC, {ABC)=iBC…
Geometry
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